Digital control device and program

ABSTRACT

A digital control device for tracking a sine wave according to the present invention has a compensator, a control object and a feedback gain. An input into the compensator is a signal obtained by subtracting a control quantity from a reference value. An input into the control object is a signal obtained by subtracting an output of the feedback gain from an output of the compensator. A transfer function of the compensator is (k 2 z+k 1 )/(z 2 −2z cos ωT+1), where ω is an angular frequency, T is a sampling period, z is a z operator, and k 1  and k 2  are constants. Thus, a second-order compensator can be configured, with which a sinusoidal reference waveform can be tracked simply and with high accuracy.

TECHNICAL FIELD

The present invention is related to a sine-wave tracking digital controldevice for controlling the power factor of a sine-wave PWM inverter orconverter, for example.

BACKGROUND ART

The output voltage waveform of voltage inverters for vector control ofAC electric motors by large power voltage inverters is not a sine wavebut a PWM modulated rectangular wave. Consequently, there is the problemof waveform distortion due to higher harmonics.

To address this problem, various devices for digitally controlling sinewave tracking have been proposed. FIG. 5 is a diagram showing the systemconfiguration of such a digital control device for sine wave tracking.This digital control device is configured by a compensator, a controlobject, and a feedback gain (h). The compensator is provided forcontrolling the tracking of the output y[i] of the control object to areference waveform y_(r)[i].

Ordinarily, an integrator as shown in FIG. 6 is often used for thecompensator in FIG. 5. However, even when performing compensation withthis integrator, sine-wave tracking control is not possible, anddeviations occur. With the control device in FIG. 6, when determiningthe gain by deadbeat control for a second-order control object, andtrying to track a sine wave, a result as shown in FIG. 7 is obtained.The width between the two curves in FIG. 7 shows the deviation betweenthe sinusoidal reference waveform and the control result with thecontrol device in FIG. 6. FIG. 8 shows a graph in which the samplepoints of the initial portion 11 in FIG. 7 have been enlarged. Asbecomes clear from FIG. 8, a deviation occurs with the control device ofFIG. 6.

On the other hand, there are also configurations provided with acompensator due to repetitive control as shown in FIG. 9, based on theinternal principle model. However, with a compensator using thisrepetitive control, a configuration becomes necessary whose ordercorresponds to one cycle. Therefore, in order to control a 50 Hz sinewave with a sample time of 100 μS (microseconds), a compensator of the200^(th) order becomes necessary. It should be noted that the “200” ofthe “200^(th) order” is calculated by “( 1/50)/0.0001).” An explanationof repetitive control is given for example in “KISO DIGITAL SEIGYO(Basic Digital Control),” Corona Publishing, p. 108.

DISCLOSURE OF THE INVENTION

A digital control device for tracking a sine wave according to thepresent invention has a compensator, a control object and a feedbackgain, wherein an input into the compensator is a signal obtained bysubtracting a control quantity from a reference value, wherein an inputinto the control object is a signal obtained by subtracting an output ofthe feedback gain from an output of the compensator, and a transferfunction of the compensator is (k₂z+k₁)/(z²−2z cos ωT+1), where ω is anangular frequency, T is a sampling period, z is a z operator, and k₁ andk₂ are constants. Thus, a second-order compensator can be configured,with which a sinusoidal reference waveform can be tracked simply andwith high accuracy.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram showing the configuration of a control deviceaccording to a preferred embodiment.

FIG. 2 is a graph illustrating the tracking of a sine wave in apreferred embodiment.

FIG. 3 is a block diagram showing the configuration of a control deviceaccording to a preferred embodiment.

FIG. 4 is a block diagram showing the configuration of a control deviceaccording to a preferred embodiment.

FIG. 5 is a block diagram showing the configuration of a control deviceaccording to the prior art.

FIG. 6 is a block diagram showing the configuration of a control deviceaccording to the prior art.

FIG. 7 is a graph illustrating the tracking of a sine wave according tothe prior art.

FIG. 8 is a magnification of the graph illustrating the tracking of asine wave according to the prior art.

FIG. 9 is a block diagram showing the configuration of a control deviceaccording to the prior art.

BEST MODE FOR CARRYING OUT THE INVENTION

The following is an explanation of an embodiment, with reference to theaccompanying drawings. FIG. 1 is a block diagram showing theconfiguration of a control device according to the present invention.

This control device 11 is a sine-wave tracking digital control devicehaving a compensator 111, a control object 112 and a feedback gain 113.

Let y_(r)[i] be the reference value and y[i] be the output of thisdigital control device. In this case, the input into the compensator 111is the value obtained by subtracting the output y[i] from the referencevalue y_(r)[i]. The input into the control object 112 is the valueobtained by subtracting the output of the feedback gain 113 from theoutput of the compensator 111. The input into the feedback gain 113 is astate variable x[i] from the control object 112.

The specific configuration of the compensator 111 is as follows: Thecompensator 111 has a first delay element 1111, a second delay element1112, a first multiplier 1113, a second multiplier 1114, and a thirdmultiplier 1115.

Here, the first delay element 1111 and the second delay element 1112delay an input by one sample period T. The first multiplier 1113multiplies an input by 2 cos ωT. 2 cos ωT means “2×(cos(ωT)).” It shouldbe noted that ω is the angular frequency, and T is the sampling period.The second multiplier 1114 multiplies an input by k₁. k₁ is a constant.The third multiplier 1115 multiplies an input by k₂. k₂ is a constant.

The input into the first delay element 1111 is the value obtained byadding the output of the first multiplier 113 to the value (e[i])obtained by subtracting the control quantity (y[i]) from the referencevalue (y_(r)[i]) of the control object, and subtracting therefrom theoutput of the second delay element 1112. The input into the second delayelement 1112, the first multiplier 1113 and the third multiplier 1115 isthe output value of the first delay element 1111. The input into thesecond multiplier 1114 is the output value of the second delay element1112. Moreover, the output of the compensator 111 is a value obtained byadding the output of the second multiplier 1114 to the output of thethird multiplier 1115.

The constants k₁ and k₂ are determined based on the control object. Theconstants k₁ and k₂ can be determined using deadbeat control or optimalcontrol. Deadbeat control and optimal control are well-known techniques,so that their further explanation has been omitted.

With this control device 11, a control tracking a sine wave as shown inFIG. 2 becomes possible. That is to say, FIG. 2 is graph correspondingto FIG. 8. According to FIG. 2, the deviation to the sine wave becomeszero at the fourth sample point of the initial portion 11.

With the present embodiment as described above, it is possible tocontrol the tracking of a sinusoidal reference waveform easily, quicklyand accurately with a second-order compensator.

It should be noted that in the present embodiment, if the constants (k₁and k₂) of the compensator in FIG. 1 have a constant ratio, then theresults in the above-noted FIG. 2 can be attained. Moreover, there is nolimitation to the specific values of the coefficient “2 cos ωT” of thefirst multiplier of the compensator and the feedback gain “1” (in FIG.1, the signal is directly put through), as long as the ratio betweenthem is “2 cos ωT:1.”

The effect of the present embodiment is not necessarily attained only bythe configuration of the compensator in FIG. 1 as described above. Inorder to attain the effect of the present embodiment, the transferfunction of the compensator should be as given in the followingequation. The effect of FIG. 2 is attained if the transfer function ofthe compensator is as given below.

That is to say, when the angular frequency is ω, the sampling period isT, z is the z operator, and k₁ and k₂ are constants, then theabove-noted effect can be attained if the transfer function of thecompensator is (k₂z+k₁)/(z²−2z cos ωT+1). It should be noted that the“2z cos ωT” in this transfer function means “2×z×(cos(ωT))”.

Moreover, in the foregoing, applications for the sine-wave trackingdigital control device according to the present embodiment have not beenmentioned, but the sine-wave tracking digital control device accordingto the present embodiment can be utilized for control of the powerfactor of a sine-wave PWM inverter or converter, for example.

Consequently, the method of sine-wave tracking digital control of thepresent embodiment can be applied to various kinds of electronicappliances. Here, electronic appliances refers to air-conditioners,washing machines, refrigerators, inverter-driven vehicles (such astrains and cars) and the like. That is to say, the method of sine-wavetracking digital control of the present embodiment can be utilizedwidely for power source control in air-conditioners, washing machines orrefrigerators, or in inverter-driven vehicles (such as trains and cars)and the like.

Moreover, if control is performed by combining the method of sine-wavetracking digital control of the present embodiment, then the control forthe tracking of a reference wave that is a combination of sine wavesbecomes possible. That is to say, when the reference wave is realized bya combination of a plurality of sine waves, then a compensator asexplained in the present embodiment may be configured for each of thosesine waves, and the various compensators may be connected in parallel.The effects noted above can also be attained for other circuitconfigurations with the same transfer function as in a parallel circuit.

The following is a more specific explanation of an example of a trackingcontrol device for the case that the reference waveform is realized by acombination of a plurality of sine waves. The following describes thecase of a three-phase reference waveform, which is “A sin ωt+(A/6)×sin3ωt”. Here, “A” is a constant, “ω” is the angular frequency, and “t” isthe time variable. Moreover, “A sin ωt” means “A×(sin(ωt))”, and “sin3ωt” means “sin(3ωt)”.

The transfer function of the compensator corresponding to the “A sin ωt”in this reference waveform is (k₂z+k₁)/(z²−2z cos ωT+1), as noted above.The transfer function of the compensator corresponding to the “(A/6)×sin3ωt” in this reference waveform is (k₄z+k₃)/(z²−2z cos ωT+1). Here, k₄and k₃ are constants. Moreover, z is the z operator. “2z cos 3ωT+1”means “(2z)×(cos(3ωT)+1).”

FIG. 3 is a block diagram showing the configuration of the controldevice for this case. As shown in FIG. 3, a compensator having thetransfer function “(k₂z+k₁)/(z²−2z cos ωT+1)” and a compensator havingthe transfer function “(k₄z+k₃)/(z²−2z cos 3ωT+1)” are connected inparallel.

The following is a generalization of the foregoing: Consider a digitalcontrol device tracking a reference waveform that is configured by acombination of n sine waves (where n is an integer of 2 or greater). Inthis digital control device, n compensators are connected in parallel,the input into the n compensators is the signal obtained by subtractingthe control quantity from the reference value, and the input into thecontrol object is the signal obtained by subtracting the output of thefeedback gain from the sum of the outputs of the n compensator. When thez operator is z, and k₁ and k₂ are constants, and when a given sine waveconstituting the reference waveform is expressed by “A sin kωt” (where Aand k are constants, ω is the angular frequency and t is the timevariable), then the transfer function of the compensator correspondingto that sine wave is (k₂z+k₁)/(z²−2z cos kωT+1). This is visualized inFIG. 4. Here, the “2z cos 2kωT” of the transfer function means“2×z×(cos(2×k×ω×T)). It should be noted that the digital control devicesshown in FIG. 3 and FIG. 4 can be utilized for controlling the powerfactors of sine-wave PWM inverters or converters, for example.Consequently, also the digital control device shown in FIG. 3 and FIG. 4can be applied to various kinds of electronic appliances. Here,electronic appliances refers to air-conditioners, washing machines,refrigerators, inverter-driven vehicles (such as trains and cars) andthe like. That is to say, the digital control device and the digitalcontrol method of FIG. 3 and FIG. 4 can be utilized widely for powersource control in air-conditioners, washing machines or refrigerators,or in inverter-driven vehicles (such as trains and cars) and the like.

In the control device in FIG. 4, n compensators are used. However, oneor more compensators are sufficient. That is to say, it is also possibleto freely bundle the n compensators in FIG. 4 and to replace them by oneor more compensators having an overall equivalent transfer function. Inthis case, the control device has the following configuration: A digitalcontrol device tracking a reference waveform that is made up bycombining n sine waves (where n is an integer of 2 or greater), thedigital control device having at least one compensator, a control objectand a feedback gain, wherein an overall transfer function of the atleast one compensator is equivalent to the overall transfer function ofthe n compensators in FIG. 4.

Moreover, in this embodiment, a digital control device was explainedthat tracks a reference waveform which is a sine wave or a combinationof sine waves. However, the digital control device or the digitalcontrol method explained in the present embodiment (the digital controldevices and the digital control methods shown in FIG. 1, 3 or 4) canalso be applied for the case that the reference waveform is acombination of sine waves and other waveforms (that are not sine waves).That is to say, if the reference waveform is a combination of sine wavesand other waveforms, the digital control devices and the digital controlmethods shown in FIG. 1, 3 or 4 can be used in the tracking control ofthe portion corresponding to the sine waves. Thus, it is possible tocontrol the tracking of the reference waveform easily and with highaccuracy.

Furthermore, it is also possible to realize the operation of the digitalcontrol device explained in the present embodiment by software. It isfurther possible to place this software on a server, for example, and todistribute the software by software downloads. Furthermore, it is alsopossible to record and distribute the software on a recording medium,such as a CD-ROM. More specifically, such a program may have thefollowing configuration: A program for realizing a digital controldevice having a compensator, a control object and a feedback gain, whichis a program for executing on a computer a digital control method fortracking a sine wave, wherein an input into the compensator is a signalobtained by subtracting a control quantity from a reference value, aninput into the control object is a signal obtained by subtracting anoutput of the feedback gain from an output of the compensator, and atransfer function of the compensator is (k₂z+k₁)/(z²−2z cos ωT+1), whereω is an angular frequency, T is a sampling period, z is a z operator,and k₁ and k₂ are constants.

The program may also be configured as follows: A program for realizing adigital control device having n compensators, a control object and afeedback gain, which is a program for executing on a computer a digitalcontrol method for tracking a reference wave that is made up bycombining n sine waves (where n is an integer of 2 or greater), whereinthe n compensators are connected in parallel, an input into the ncompensators is a signal obtained by subtracting a control quantity froma reference value, an input into the control object is a signal obtainedby subtracting an output of the feedback gain from a sum of the outputsof the n compensators, and when a given sine wave constituting thereference waveform is expressed by “A sin kωt” (where A and k areconstants, ω is the angular frequency and t is the time variable), thena transfer function of the compensator corresponding to that sine waveis (k₂z+k₁)/(z²−2z cos kωT+1), where z is a z operator, and k₁ and k₂are constants.

The program may also be configured as follows: A program for realizing adigital control device having at least one compensator, a control objectand a feedback gain, which is a program for executing on a computer adigital control method for tracking a reference wave that is made up bycombining n sine waves (where n is an integer of 2 or greater), whereinan overall transfer function of the at least one compensator isequivalent to the overall transfer function of the n compensators inFIG. 4.

INDUSTRIAL APPLICABILITY

The present invention is related to a sine-wave tracking digital controldevice for controlling the power factor of a sine-wave PWM inverter orconverter, for example, and can control the tracking of a sinusoidalreference wave easily and with high accuracy, with a second-ordercompensator.

1. A sinusoidal wave follow-up digital control device for use with PWMinverters for tracking a sine wave, said digital control devicecomprising a compensator, a control object to be controlled by thesinusoidal wave follow-up digital control device and a feedback gaincontrol, wherein the compensator is configured to receive as its input asignal obtained by subtracting a control quantity from a referencevalue; wherein the control object is configured to receive as its inputa signal obtained by subtracting an output of the feedback gain controlfrom an output of the compensator; and wherein a transfer function ofthe compensator is (k₂z+k₁)/(z²−2z cos ωT+12), where ω is an angularfrequency, T is a sampling period, z is a z operator, and k₁ and k₂ areconstants, thereby configuring a second-order compensator for providinghigh accuracy tracking of a sinusoidal reference waveform.
 2. Thesinusoidal wave follow-up digital control device according to claim 1,wherein the compensator comprises a first delay element outputting aninput at a delay of one sample period T, a second delay elementoutputting an input at a delay of one sample period T, a firstmultiplier multiplying an input by 2z cos ωT, a second multipliermultiplying an input by k₁, and a third multiplier multiplying an inputby k₂; wherein the first delay element is configured to receive as itsinput a signal obtained by adding an output of the first multiplier tothe signal obtained subtracting the control quantity from a referencevalue of the control object, and subtracting from this added signal theoutput of the second delay element; wherein the second delay element,the first multiplier and the third multiplier are configured to receiveas their inputs an output from the first delay element; wherein thesecond multiplier is configured to receive as its input a signal that isoutput from the second delay element; and wherein the compensatoroutputs a signal that is obtained by adding an output of the secondmultiplier to an output of the third multiplier.
 3. A sinusoidal wavefollow-up digital control device for tracking a reference waveform madeup by combining n sine waves (where n is an integer of 2 or greater),the digital control device having n compensators, a control object and afeedback gain control; wherein the n compensators are connected inparallel; wherein the n compensators is configured to receive as itsinput a signal obtained by subtracting a control quantity from areference value; wherein the control object is configured to receive asits input a signal obtained by subtracting an output of the feedbackgain control from a sum of the outputs of the n compensators; andwherein, when a given sine wave constituting the reference waveform isexpressed by “A sin kωt” (where A and k are constants, ω is an angularfrequency and t is a time variable), then a transfer function of thecompensator corresponding to that sine wave is (k₂z+k₁)/(z²−2z coskωT+1), where z is a z operator, and k₁ and k₂ are constants.
 4. Asinusoidal wave follow-up digital control device for tracking areference waveform made up by combining n sine waves (where n is aninteger of 2 or greater), the digital control device having at least onecompensator, a control object and a feedback gain control; wherein anoverall transfer function of the at least one compensator is equivalentto the overall transfer function of the n compensators of claim
 3. 5. Anelectronic appliance incorporating the sinusoidal wave follow-up digitalcontrol device according to any one of claims 1 to
 4. 6. A programproduct stored on a computer readable medium for realizing a sinusoidalwave follow-up digital control device having a compensator, a controlobject and a feedback gain control, the program executing on a computera digital control method for tracking a sine wave; wherein thecompensator is configured to receive as its input a signal obtained bysubtracting a control quantity from a reference value; wherein thecontrol object is configured to receive as its input a signal obtainedby subtracting an output of the feedback gain control from an output ofthe compensator; and wherein a transfer function of the compensator is(k₂z+k₁)/(z²−2z cos ωT+1), where ω is an angular frequency, T is asampling period, z is a z operator, and k₁ and k₂ are constants.
 7. Aprogram product stored on a computer readable medium for realizing asinusoidal wave follow-up digital control device having n compensators,a control object and a feedback gain control, the program executing on acomputer a digital control method for tracking a reference waveform madeup by combining n sine waves (where n is an integer of 2 or greater);wherein the n compensators are connected in parallel; wherein the ncompensators is configured to receive as its input a signal obtained bysubtracting a control quantity from a reference value; wherein thecontrol object is configured to receive as its input a signal obtainedby subtracting an output of the feedback gain control from a sum of theoutputs of the n compensators; and wherein, when a given sine waveconstituting the reference waveform is expressed by “A sin kωt” (where Aand k are constants, ω is an angular frequency and t is a timevariable), then a transfer function of the compensator corresponding tothat sine wave is (k₂z+k₁)/(z²−2z cos ωT+1), where z is a z operator,and k₁ and k₂ are constants.
 8. A program product stored on a computerreadable medium for realizing a sinusoidal wave follow-up digitalcontrol device having at least one compensator, a control object and afeedback gain control, the program executing on a computer a digitalcontrol method for tracking a reference waveform made up by combining nsine waves (where n is an integer of 2 or greater); wherein an overalltransfer function of the at least one compensator is equivalent to theoverall transfer function of the n compensators of claim 7.